If $A$ travels to his school from his house at the speed of $3 \, km/h$,he reaches the school $5 \, minutes$ late. If he travels at the speed of $4 \, km/h$,he reaches the school $5 \, minutes$ earlier than the scheduled time. The distance of his school from his house is (in $km$):

$A$ dog finds a cat at $25$ leaps away. The cat sees the dog coming towards it and starts running with the dog in hot pursuit. In every minute, the dog makes $5$ leaps and the cat makes $6$ leaps, and one leap of the dog is equal to $2$ leaps of the cat. Find the time in which the dog will catch the cat (in minutes).

$50$ trees are standing in a line such that the distance between any two consecutive trees is the same. $A$ car takes $18 \, seconds$ to travel from the $13^{th}$ tree to the $34^{th}$ tree. How much time (in $seconds$) will it take to reach from the first tree to the $50^{th}$ tree?

$A$ man standing on a railway platform observes that a train going in one direction takes $4 \,seconds$ to pass him. Another train of the same length going in the opposite direction takes $5 \,seconds$ to pass him. The time taken (in $seconds$) by the two trains to cross each other will be:

$A$ person goes from point $A$ to $B$ with a speed of $55 \text{ km/hr}$ and returns with a speed of $65 \text{ km/hr}$. What is the average speed (in $\text{km/hr}$) of the person while going and coming back from $A$ to $B$?

$A$ man is walking at a speed of $10 \, km/h$. After every $1 \, km$, he takes a rest for $5 \, minutes$. How much time will he take to cover a distance of $5 \, km$? (in $minutes$)